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1. 2^6=64

2.4^-3= 1/64

1. log2(32)=5

2.log10(0.1)= -3

1. 3

2.2

1. log5(3) + log5(x)

2. log2(x) - log2(5)

3. log(x) + 2log(y)

4. log4(x) + log4(y) - log4(3)

1.log5(7) - log3(x) <-- nothing can be done

2. log5(3x^2)

3.log4(5xy)

4.log(x^3/4)

See below

Step-by-step explanation:

log2(64)=6 would be the same as 2^6=64 as log2(x)=y is the same as 2^y=x

Now we can apply this same rule to the other one:

log4(1/64)=-3 would be the same as 4^-3=1/64

From 2^5=32 to logarithmic form is the reverse process. It would be log5(32)=2 if you refer to earlier.

Same deal with 10^-1=0.1, it becomes log10(0.1)=-1

log2(8) would be equal to 3 because we are solving 2^x=8 which is 3.

log8(64) would be equal to 2 because we are solving 8^x=64 which is 2.

log5(3x) is the same as log5(3)+log5(x) as the addition of logarithms in the same base is the same as multiplying the numbers in the parenthenses.

log2(x/5) is the same as log2(x)-log2(5) as the subtraction of logarithms in the same base is the same as dividing the numbers in the parenthenses.

log10(xy^2) would be log10(x)+2log10(y)

log4(xy/3) would be [log4(x)+log4(y)]/[log4(3)] because now we are using BOTH properties. log4(xy)/log4(3) becomes [log4(x)+log4(y)]/[log4(3)]

log3(7)-log3(x)=log3(7/x) using division property of logarithms

2log5(x)+log5(3)=log5(3x^2) using exponent property of logarithms and multiplication property of logarithms. The 2 becomes the exponent for the x in other words.

log4(5)+log4(x)+log4(y)=log4(5xy) using multiplication property of logarithms

3log10(x)-log10(4)=log10(x^3/4) using exponent and division properties of logarithms

Hope these give you a better understanding of the properties of logarithms!

step-by-step explanation:

from the graph attached below:

domain of graph is the value of x for which the given function profit function p(x) is defined.

(a) the domain represents the number of years for which the outlet will earn a profit.

range of profit function defines the lowest to highest value of profit earned.

(b) the range of this function is (0 , 160 ). for this function, the range represents the outlet's profit earned.